1. Field of the Invention
This invention relates to a method for the determination of biomass in a medium, in particular a medium containing biological cells. It also relates to a device for the implementation of this method, as well as a measurement device implementing this method, which can be used for a biomass measurement.
This is a method for determining dielectric characteristics, which on the one hand makes it possible to correct the main sources of errors encountered in the impedance measurements used for conductive media, and on the other hand to obtain parameters characterizing the β dispersion of biological cell suspensions.
2. Description of the Related Art
Measurements of electrical impedance, and in particular of dielectric permittivity, can be used in order to obtain in non-destructive manner information on the composition or structure of the media studied. Measurement of the biomass concentration in fermentation media is one example of the application of this technique. This measurement, which has now become practically a routine measurement, has resulted from a two-phase development.
A first phase, up to the end of the 1970s, made it possible for scientists to study the electrical properties of biological media and cell suspensions, and to show the relationship between cell concentration and dielectric permittivity. It is known from the work of researchers such as for example Fricke (1953, “Relation of the permittivity of biological cell suspensions to fractional cell volume” which appeared in Nature, 172, 4381, 731-732) and Schwann, (1957, “Electrical properties of tissues and cell suspensions” which appeared in Adv. Biol. Med. Phys., 5, 147-209), that a strong correlation exists between permittivity, measured in the radio frequency range and volume fraction of cells (yeasts, red blood cells etc.) in the medium studied. In fact, when a living cell is subjected to an electric field, the displacement of the ions inside the cell is limited by the cytoplasmic membrane, which induces a polarization phenomenon. Each cell then behaves like a small capacitor. The amplitude of this polarization, which can be evaluated by measuring the dielectric permittivity (or capacitance) of the medium, depends on the frequency of the electric field applied. At relatively high frequencies, of the order of 10 MHz and above, polarization is weak. The dielectric permittivity (and the capacitance) then substantially corresponds to that of medium devoid of cells. In contrast, at relatively low frequencies, of the order of 0.1 MHz, the cells are completely polarized, and the dielectric permittivity (and the capacitance of the suspension) is higher. This phenomenon, which therefore relates to measurements carried out in the so-called “radio” frequency range, is described in the scientific literature under the name of B dispersion. The form of this dispersion is characteristic, as illustrated by FIG. 1, the permittivity progressively reducing from a low frequency plateau to a high frequency plateau, following a reversed S-shaped curve. The mathematical relationship between biovolume and dielectric permittivity has been established. For spherical cells, the dielectric increment Δ∈, established by finding the difference between the permittivity ei measured at low frequency and that eh measured at higher frequency, is proportional to the product P·t·Cm, an expression in which P is the volume fraction occupied by the biomass, r is the radius of the cells, assumed to be spherical, and Cm is the membrane capacitance, according to the relationship
            Δ      ⁢                          ⁢      ɛ        =                  9        ⁢                                  ⁢                  PrC          m                            4        ⁢                  e          0                      ,
As the cell volume is almost proportional to the cell mass, it is thus possible, by means of two measurements carried out at two frequencies on either side of the B dispersion range, to simply evaluate the concentration of microorganisms (bacteria, yeasts, animal cells etc.) in a culture medium.
Siugura et al., in the article “Dielectric behavior of yeast cells in suspension”, which appeared in J. Gen. App. Microbiol., 10, 2, 163-174 (1964), have thus presented without ambiguity the linear experimental relationship between the dielectric increment, measured in a frequency range corresponding explicitly to the B dispersion, and the volume fraction of suspensions of Saccharomyces. 
Up to the end of the 1970s, published works were most often concerned only with the study of “model” suspensions of cells in “ideal” media, water or saline solutions at low concentrations. In fact, the measurements, which most often used capacitance bridges with manual adjustment and platinated platinum electrodes, were tedious and difficult, thus preventing any practical development outside research laboratories. As discussed below, one of the main difficulties encountered by the experimenters was the polarization of the surface of the electrodes, which is capable of significantly disrupting the capacitance measurements. In spite of this, Gencer and Mutharasan, in the article “Determination of biomass concentration by capacitance measurement” which appeared in 1979 in the journal Biotechnol. Bioeng., 21, 6, 1097-1103, showed the benefit of capacitance measurements used for monitoring fermentations in situ and in real time.
The second phase commenced at the end of the 1970s, thanks to progress in electronics and the development of automated devices, in particular by Hewlett-Packard, which then radically changed the situation by simplifying the implementation of capacitance measurements, thus allowing their popularization. (T. Ichino (HP) and H. Ohkawara (HP) and N. Sugihara (HP). Vector impedance analysis to 1000 MHz. Hewlett-Packard Journal: technical information from the laboratories of Hewlett-Packard Company, 31 (1), pp. 22-31, January 1980; Y. Narimatsu (HP) and K. Yagi (HP) and T. Shimizu (HP). A versatile low-frequency impedance analyzer with an integral tracking gain-phase meter. Hewlett-Packard Journal: technical information from the laboratories of Hewlett-Packard Company, 32 (9), pp. 22-28, September 1981).
Clarke et al., in the article “Sensors for bioreactor monitoring and control—a perspective”, published in J. Biotechnol, 1, 135-158, were among the first to explicitly mention the benefit of the technique for determining biomass concentration in fermentation, and propose a device making it possible, starting with a permittivity measurement, to monitor the growth of microbial cultures.
EP0282532 describes a method for measuring biomass which makes it possible, starting with a capacitance measurement carried out at a single frequency, chosen from the low-frequency range of the B dispersion, to obtain a signal representative of the biovolume. This method makes it possible to avoid measurements at multiple frequencies, which are necessary for estimating the amplitude of the β dispersion.
On the other hand, as indicated by the inventor himself (Yardley, KeIl et al., 2000. On-line, real-time measurements of cellular biomass using dielectric spectroscopy, published in Biotechnology & Genetic Engineering Reviews, vol. 17, 2000, Pages 3-35), it is necessary to have a reference measurement obtained before the start of fermentation, in order to be able to evaluate the capacitance variation. The main drawback of this method is therefore its sensitivity to the errors linked to parasitic capacitance variations, as a function of time, frequency and conductivity of the medium, due to the polarization of the electrodes or to different imperfections in the materials used.
EP0281602, filed jointly with the preceding patent, presents a device for measuring the capacitance of a fermentation medium, which uses a technique for measuring the amplitude of the in-quadrature and in-phase demodulated signal;
EP0620919 describes a method for measuring gas hold-up with a device operating according to the principles described in the patent EP0281602, which uses two intensity measurements of the reactive current at a high frequency, one carried out before fermentation, the other during fermentation, the result being used to correct the biomass measurement;
If the measurement principle is simple, its implementation is rendered complex because of the influence of several variables, which act not only on the amplitude of the dielectric increment, but also on the general shape of the β dispersion curve. The expression generally adopted to describe this dispersion is the following
  ɛ  =            ɛ      h        +                            Δ          ⁢                                          ⁢          ɛ          ⁢                                          ⁢          1                +                                            f                              1                -                α                                                    f              c                                ⁢          sin          ⁢                                          ⁢          α          ⁢                      π            2                                      1        +                              f                          2              ⁢                              (                                  1                  -                  α                                )                                                          f            c                          +                  2          ⁢                                    f                              1                -                α                                                    f              c                                ⁢          sin          ⁢                                          ⁢          α          ⁢                      π            2                              
The point of inflexion of this curve, situated at mid-height between the two plateaux, corresponds to a frequency known as the characteristic frequency fc, as illustrated by FIG. 1. The gradient of the tangent at the point of inflexion depends on the superposition of several dispersions, of adjacent characteristic frequencies, induced for example by a variation in the size of the cells around an average value. The coefficient a, which makes it possible to take this phenomenon into account, is an empirical parameter known by the name Cole-Cole a dispersion factor.
The article by Yardley et al. (previously cited) examines all of the problems posed by the measurement. For example, the technical constraints mean that the measurements can generally be carried out neither at a sufficiently low frequency, nor at a sufficiently high frequency, which means that the plateaux on either side of the B dispersion zone cannot be reached. The dielectric increment cannot therefore be measured in its totality. The frequency characteristic fc is displaced under the influence of variations in the conductivity of the medium s m and the intracellular conductivity s c, the cell size r and membrane capacitance Cm, according to the relationship
      f    c    =      1                  2        ⁢                                  ⁢        π        ⁢                                  ⁢        r        ⁢                                  ⁢                  C          m                ⁢                  1                      σ            c                              +              1                  2          ⁢                                          ⁢                      σ            m                              which leads to variations in the capacitance measurement if the measurements cannot be carried out on the plateaux.
Finally, the gradient of the dispersion curve, around the characteristic frequency fc, is itself variable, as a function of the value of the a dispersion factor, which can induce variations in the measured capacitance, independent of variations in the cell concentration.
It is thus desirable to evaluate the dielectric (or capacitive) increment starting with measurements carried out at several frequencies, in order to reconstitute, optionally by extrapolating, the whole of the β dispersion curve. Impedance spectroscopy is then considered. Because of the form of the mathematical function describing the β dispersion, obtaining mathematical descriptors of the dispersion curve (Δ∈, fc, a) generally requires the implementation of so-called “non-linear” mathematical adjustment techniques, one of the best known being the Levenberg-Marquard iterative method.
These techniques are costly in terms of computing power (or time). Moreover, it is generally necessary to provide a starting value at different parameters in order that the iterative method converges towards a suitable solution. These techniques cannot therefore be implemented economically in microcontroller-based measurement systems, as encountered in numerous commercial measurement devices.
To these difficulties is added that linked to electrode surface polarization. In fact, in the impedance measurement systems using electrodes in direct contact with the medium, the measurement of the characteristics specific to the medium is disturbed in particular by the accumulation of charges at the surface of the electrodes, which causes a systematic polarization phenomenon. The capacitance which results from this is added to that of the medium and develops with the ionic conductivity of the medium. A second source of error is linked to the adsorption of compounds in solution on the electrodes. This adsorption causes a modification of the electric properties of the metal-liquid medium interface, which depending on the type of molecules adsorbed, results in a variation in capacitance, the direction and amplitude of which cannot be foreseen, and which we shall call random polarization. In practice, the amplitude of random polarization is clearly smaller than that of systematic polarization.
These problems are well known, and several methods have been proposed, in particular by Schwan in 1963 in his article “Determination of biological impedances”, published in “Physical techniques in Biological research”, vol 6, Nastuk ed., Academic Press, pp. 323-407, either to limit the polarization amplitude (modification of the state of the surface of the electrodes, systems with 4 electrodes, liquid electrodes), or to evaluate the polarization amplitude (variation in the inter-electrode distance), or to evaluate and correct, by calculation, the contribution of polarization of the electrodes. Theoretically, this last operation is possible because polarization of the surface of the electrodes diminishes rapidly with the measurement frequency. By carrying out a few measurements at low frequencies, it is possible to evaluate the polarization capacitance at higher frequencies, providing that its law of variation with frequency is known. A law of the typeCpol=C0pol−f−k is generally used, in which k is an experimental coefficient generally comprised between 1 and 2. It is then possible to correct the capacitance measurements by subtracting from them this estimation of the polarization capacitance.
Thus, Sugiura et al. describe, in the article “Dielectric behavior of yeast cells in suspension”, J. Gen. App. Microbiol., 10, 2, 163-174 (1964), a correction of the capacitance measured in a suspension of yeasts, in which measurements carried out at low frequency were used in order to correct those carried out at higher frequencies.
Bordi et al. have proposed, in the article “Reduction of the contribution of polarization effects in the radiowave dielectric measurements of highly conductive biological cell suspension”, Biolectrochemistry 2001, a global non-linear adjustment method which allows the contribution of the capacitance of the electrodes to be eliminated.
The document EP0282532 (KeIl) discloses an equivalent method, referred to as method 2f, which uses the relationship of the capacitance measurements carried out at two frequencies in the low part of the β dispersion, a frequency range where the influence of the polarization of the electrodes is predominant compared with that of the capacitance of the cell suspension. The drawback of this last method is that it explicitly assumes that the polarization of the electrodes follows a single fixed law, independent of the conductivity of the medium, and above all that it does not take into account the errors due to imperfections in the materials used.